196 SURFACES AND MEMBRANES 



sodium chloride is apparently not completely dissociated. Table V-5 

 shows that its degree of ionization a is 77 per cent, that this degree of 

 ionization increases with dilution, and that only at infinite dilutions 

 would one expect the degree of ionization to be 100 per cent. The os- 

 motic pressure of a 0.5 M sodium chloride solution is due to 77 positive 

 ions, 77 negative ions, and 23 undissociated molecules per 100 sodium 

 chloride molecules found in the solvent at this concentration. These 

 ions additively develop an osmotic pressure equal to 1.77 times 12.8 or 

 22.7 atmospheres. 



Isotonic Coefficient 



The van't Hoff isotonic coefficient 00 is a number by which the 

 osmotic pressure, calculated from the general gas law, must be multiplied 

 in order to give the expected osmotic pressure of an acid, base, or salt. 



If n is the number of ions into which the molecule dissociates when 

 introduced into a solvent and a is the fraction of the molecules ionized 

 at a given concentration, called the degree of ionization, then the isotonic 

 coefficient is defined by 



i = na + (1 — a) 



Table V-5 shows some typical results obtained from sodium chloride 

 dissolved in water; of special importance is the fact that the isotonic 

 coefficient increases with dilution because of the increase in degree of 

 ionization. Only for very dilute solutions (C < 0.0001) is the dissocia- 

 tion so complete that each molecule appears as two ions in the solvent to 

 produce the expected osmotic pressure. 



The Freezing Point 



The construction of an adequate semi-permeable membrane with 

 which to determine the osmotic pressure of most physiological liquids 

 has often entailed insurmountable difficulties. An indirect method can 

 be resorted to which will give adequate quantitative results. Advan- 

 tage is taken of the relation that exists between the freezing point of a 

 solution and its molal concentration on the one hand and its molal 

 concentration and osmotic pressure on the other hand. 



The temperature at which a liquid substance exists in equilibrium 

 with its solid crystalline state is termed its freezing 'point. This must 

 not be confused with the melting point; for instance, a fat like mutton 

 tallow solidifies between 36° and 41° C, but melts around 44° C; butter 

 solidifies near 21.5° C, but melts at about 30° C. 



Both the melting point of ice and the freezing point of water are 0° C 

 under standard conditions. 



